Principal component analysis can be computed through the singular
value decomposition (SVD) [1]}, [2]}, [3]} as follows.
The \(n\)  observations \(y_i \in \mathbb {R}^p\)  are mean-centered by subtracting
their average \(\bar{y} = \dfrac{1}{n} \sum ^{n}_{j=1} y_{j}\) .
The new data vectors \(x_{i} = y_{i}-\bar{y}\)  form the columns of the \(p\times n\) 
data matrix \(X\)  whose singluar value decomposition is given by
\(X = U \Sigma V^\top ,\) 
